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People
Guifre Vidal	Jo Hughes	Do you want to join us?
(Professor)	(Admin Assistant)	Prospective PhD Students
ARC Fed Fellow
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Blank Line
Roman Orus	Richard Davis	Ian McCulloch
(PostDoc)	(PostDoc)	(PostDoc)
2D Systems	1D Systems	DMRG
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Glen Evenbly	Jacob Jordan	Sukhwinder Singh
(PhD Student)	(PhD Student)	(PhD Student)
MERA	2D Systems	Symmetries
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Main research areas

Quantum Information Science: entanglement and tensor network representations in quantum lattice systems.

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Quantum Many-Body Physics: emergent phenomena in strongly correlated systems, quantum phase transitions, topological order.

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Computational Quantum Physics: efficient algorithms to simulate quantum lattice systems.

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Overview
Research in our group revolves around the study of many-body entanglement. This is a fascinating, quite recent - and therefore still relatively unexplored - research area, with the potential for plenty of further discoveries. It naturally bridges between quantum information science, condensed matter physics and computational physics.

Quantum computers can, in principle, efficiently solve certain problems for which the best known classical algorithm is not efficient. But what makes quantum systems (potentially) more powerful than classical systems? While this is not yet well-understood, it has been established in recent years that entanglement plays a fundamental role in any quantum computational speed-up [1]. Indeed, we now know that in the absence of a sufficiently large amount of entanglement, a quantum computer can be efficiently simulated with a classical computer. Thus, entanglement is a necessary ingredient for quantum computation.

In recent times, however, it has become increasingly evident that the influence of entanglement theory goes well beyond the area of quantum information and computation. On the one hand, entanglement is the guiding principle that has produced a novel characterization of quantum many-body phenomena in condensed matter physics [2]. On the other, progress in our understanding of entanglement has also led to breakthrough simulation algorithms for strongly correlated systems in the area of computational physics, by using tensor networks [3]. Our group at UQ has pioneered these developments and is firmly established among the leading groups worldwide.

What do we do?
Given a quantum system defined on a D dimensional lattice, we investigate general principles governing the structure of entanglement in typical states of the system, such as its ground state. An example of progress in this direction includes the realization that the ground state can be regarded as the output of a remarkably short quantum computation. The computation is performed with a quantum circuit of fixed wire structure called MERA [4]. Physical properties are encoded in the gates of the MERA and vary from system to system. But the gates in the MERA are wired according to a quantum circuit that is common to all systems. This implies that, at some qualitative level, entanglement in the ground state of most systems is organized in the same manner. In other words, as far as entanglement is concerned, most ground states are structured is a universal way.

Thus, starting with ideas from quantum computation and quantum information, one ends up deep inside the realm of condensed matter physics. The MERA and the related notion of entanglement renormalization [5] produce a novel (real space) renormalization group transformation for lattice systems in terms of which a very elegant characterization of quantum phases can be issued. In this classification, symmetry-breaking and topologically ordered quantum phases are distinguished by how they transform under the renormalization group map [6]. In turn, quantum critical points correspond to non-trivial (highly entangled) fixed points of the map [5,7].

As mentioned before, the study of entanglement also has very strong implications in the area of numerical methods for quantum many-body systems. Our group is currently developing a series of breakthrough techniques for the simulation of lattice systems. These are based on the use of tensor networks representations to efficiently represent the state of the lattice. We have developed methods using the so-called MPS in 1D systems [3,9], PEPS in 2D systems [9] and MERA for critical systems [10]. Particular emphasis has been placed in the simulation of infinite systems [7,8,9] and the exploitation of global symmetries, such as spin isotropy, which is the key to significant gains in efficiency [11].

We are witnessing a very exciting moment in the areas of condensed matter and computational physics. For the first time, we might be able to address two-dimensional lattice models for frustrated spins and fermions. These include the Hubbard and certain anti-ferromagnetic Heisenberg models, which are believed to be the key to elucidating the mechanisms for high temperature superconductivity or the existence of a spin liquid, two of the main open problems in the area of strongly correlated systems. Such lattice models have, for decades, eluded resolution by any other numerical approach. But now, thanks to recent progress in our understanding of the structure of entanglement, we have a realistic chance to finally solve these problems by using tensor network algorithms.

References
[1] Efficient classical simulation of slightly entangled quantum computations, G. Vidal, Phys. Rev. Lett. 91, 147902 (2003), quant-ph/0301063
[2] Entanglement in quantum critical phenomena, G. Vidal, J. I. Latorre, E. Rico and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003) , quant-ph/0211074
[3] Efficient simulation of one-dimensional quantum many-body systems, G. Vidal, Phys. Rev. Lett. 93, 040502 (2004), quant-ph/0310089
[4] A class of quantum many-body states that can be efficiently simulated, G. Vidal, arXiv:quant-ph/0610099
[5] Entanglement Renormalization, G. Vidal, Phys. Rev. Lett. 99, 220405 (2007), cond-mat/0512165
[6] Entanglement renormalization and topological order, M. Aguado and G.Vidal, arXiv:0712.0348[cond-mat.str-el]
[7] Entanglement renormalization in fermionic systems, G. Evenbly and G.Vidal, arXiv:0710.0692[quant-ph]
[8] Classical simulation of infinite-size quantum lattice systems in one spatial dimension, G. Vidal, Phys. Rev. Lett. 98, 070201 (2007),cond-mat/0605597
[9] Classical simulation of infinite-size quantum lattice systems in two spatial dimensions, J. Jordan, R. Orus, G. Vidal, F. Verstraete, J. I. Cirac, arXiv:cond-mat/0703788
[10] Algorithms for entanglement renormalization, G. Vidal, arXiv:0707.1454
[11] Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry, S. Singh, H.-Q. Zhou, G. Vidal, arXiv:cond-mat/0701427